利用GCV优化的正则化方法对硬X射线望远镜图象重建研究

图象重建是一个求逆过程具有不适定性。本文介绍的是一种从少数投影数据进行图象重建的线性代数法－Ｐｈｉｌｌｉｐｓ－Ｔｉｋｈｏｎｏｖ正则化方法，同时选择优化工具ＧＣＶ确定最优的正则参数。为验证该方法，我们对日本Ｙｏｈｋｏｈ卫星上塔载的硬Ｘ射线望远镜（ＨＸＴ）拍摄的太阳图象进行重建。

Phillips-Tikhonov Regularization of Hard X-ray Telescope Image Reconstruction with Generalized Cross Validation

The reconstruction of images is an inverse problem and is generally recognizable as being ill-posed. For the strong restrictions on the projection angle and projection number in imaging systems, CT for image reconstruction often suffers from numerically unstable behaviors of solutions due to the ill-conditioned systems of equation. The method discussed here is the linear algebraic method of Phillips-Tikhonov regularization about image reconstruction with sparse data. With the aid of SVD(singular value decomposition), it is possible to use GCV(generalized cross validation) for optimizing a regularization parameter( r ) . In this paper, we reconstruct hard X-ray telescope solar images in 64*64 pixels from a set of only 64 data. When GCV( r ) minimizes at r =2 and suggests the corresponding image to be optimal. With the increase of r , the reconstructed images are more smoothed but have a loss of spatial resolution. With the decrease of r , the reconstructed images have high spatial resolution.